On perpetual insurance

The main idea: proposing an insurance schedule whereby one premium is paid and cover continues indefinitely until a claim is made as a way to help with products afflicted by moral hazard. 

0. Posts on this blog are ranked in decreasing order of likeability to myself. This entry was originally posted on 25.05.2022, and the current version may have been updated several times from its original form.

1.1 Here’s the idea: insurance that requires you to pay premium once, and rolls over forever. Until you make a claim, that is, whereupon the policy lapses (the claim is still honoured of course).

1.2 To explain what value would this setup provide, let’s take the example of health insurance.

1.3 With health insurance, by the time you apply all safeguards aimed at keeping people from making spurious or just non-critical claims, you end up with a policy so complex that all flexibility and transparency is lost. And yet, health insurance only works if claimants limit themselves to making truly critical claims only, paying the rest out of pocket.

1.4 If this code is adhered too, health insurance is cheap and available when most needed. If it’s not, it balloons into hyperplanes of rules of extreme cost. Of course, each individual policyholder’s interest is in getting as much out of the policy as they can.

1.5 Whilst health insurance is the premier example I can think of, I reckon there are offering which don’t even exist because they can’t get over this particular hill. Liability insurance? Totaling your car (vs. scratching)? What else?

1.6 So, you issue the policy and get one premium, one time, and you get to make one claim. Akin to an American option, you better optimise that one claim, hence aligning your interest with those of the policyholder body as a whole.

1.7 Following a payment schedule more akin to life products, whereas you get to make one claim but must pay periodic premia, would not work because as long as the coverage runs you incur a cost. The optimal claim is thus lower than the true optimal, as by claiming you get to “save” on future premia. So, one premium, one time it is.

1.8 Notice how bad risks must pay multiple premia to retain cover, whereas good risks pay fewer premia. Automatic bonus-malus, minimal adverse selection. 

1.9 Surely, one would think that such a scheme could never make sense, as getting one premium and paying out one claim ensures very little daylight between the two, except for what the company could make by investing. How could this ever work?

1.10 Well, it can if it is applied to such events that are even rarer than death. Everyone will die once, and this product will make financial sense only if applied to claims that happen to a subset of clients once per life (and are uncorrelated, so no earthquake stuff alas). Critical illness, other stuff of the sort. So, the claim multiplies by the frequency (and divides by investment gains) into a reasonable premium.

1.11 But wait, surely policyholders will make some claim instead of letting the policy go to waste. Well, even they can get around to claiming out of spite before they pass away, they will claim something minor, since we postulate that the ideal claim is rare enough that not all people will experience it. Instead of claiming for cancer treatment since they most never get cancer, they claim some particularly expensive dental job when they hit 80.